Fig. 2. Correlation function.

a Correlation function of fMRI signals as a function of the distance between nodes. Error bars indicate SEM. The correlation function of fMRI signals was approximately power-law, i.e., $g\left(r\right)~r^{-\tilde{\eta }}$. The power law was fitted in the distance interval $r\in \left[10,90\right]$ mm. b Distribution of the estimated power exponent for single-subject scans (n = 1003). c Distribution of the relative estimation error of exponent $\tilde{\eta }$, i.e., $\mathrm{\Delta }\tilde{\eta }/\tilde{\eta }$, where $\mathrm{\Delta }\tilde{\eta }$ is the least square estimation error of exponent $\tilde{\eta }$. Note that the average relative estimation error is <3%. d The power law fit was compared the one obtained using an exponential function by calculating the ratio between the explained variance of the competing regression models. Ratios larger than 1 favor the power law hypothesis. e, f When fitting the power law to $g\left(r\right)$ in the distance interval $r\in \left[r_{\min },r_{\max }\right]$, for several combinations of $r_{\min }$ and $r_{\max }$, we found a large region in the $\left[r_{\min },r_{\max }\right]$ plane with high explained variance $R^2$ (e) yielding power exponents $\tilde{\eta }~$ 0.52 (f, the blue dotted line indicates the region for which $R^2>$ 0.95).